"""
Metrics and basic statistics for Collatz graphs.
"""

from __future__ import annotations

from typing import Dict, Any, Iterable

import pandas as pd


def _to_int_nodes(nodes: Iterable[Any]) -> list[int]:
    """
    Safely convert an iterable of node labels to a list of integers.
    Non-convertible labels are skipped.
    """
    int_nodes: list[int] = []
    for n in nodes:
        try:
            int_nodes.append(int(n))
        except Exception:
            continue
    return int_nodes


def compute_basic_graph_stats(df_edges: pd.DataFrame) -> Dict[str, Any]:
    """
    Compute basic statistics for a Collatz graph represented
    as a DataFrame of edges with columns ["Source", "Target"].

    Returns a dictionary with:
        - num_nodes: total number of distinct nodes
        - num_edges: total number of edges
        - num_odd:   number of odd-valued nodes
        - num_even:  number of even-valued nodes
        - min_node:  minimum node value (if any)
        - max_node:  maximum node value (if any)
        - num_cycles: number of cycles (here always 1: the trivial 1–2–4–1 cycle)
    """
    if not {"Source", "Target"}.issubset(df_edges.columns):
        raise ValueError("df_edges must contain 'Source' and 'Target' columns.")

    raw_nodes = set(df_edges["Source"]).union(set(df_edges["Target"]))
    nodes = _to_int_nodes(raw_nodes)

    num_nodes = len(nodes)
    num_edges = len(df_edges)

    num_odd = sum(1 for n in nodes if n % 2 == 1)
    num_even = sum(1 for n in nodes if n % 2 == 0)

    min_node = min(nodes) if nodes else None
    max_node = max(nodes) if nodes else None

    # By construction, your graphs contain only the trivial 1–2–4–1 cycle.
    num_cycles = 1 if num_nodes > 0 else 0

    return {
        "num_nodes": num_nodes,
        "num_edges": num_edges,
        "num_odd": num_odd,
        "num_even": num_even,
        "min_node": min_node,
        "max_node": max_node,
        "num_cycles": num_cycles,
    }


def format_stats_markdown(stats: Dict[str, Any]) -> str:
    """
    Format the statistics dictionary returned by compute_basic_graph_stats
    into a human-readable Markdown string for display in the UI.
    """
    if not stats:
        return "_No statistics available._"

    num_nodes = stats.get("num_nodes", 0)
    num_edges = stats.get("num_edges", 0)
    num_odd = stats.get("num_odd", 0)
    num_even = stats.get("num_even", 0)
    min_node = stats.get("min_node", None)
    max_node = stats.get("max_node", None)
    num_cycles = stats.get("num_cycles", 0)

    lines = [
        "### Graph Statistics",
        "",
        f"- **Nodes:** {num_nodes}",
        f"- **Edges:** {num_edges}",
        f"- **Odd nodes:** {num_odd}",
        f"- **Even nodes:** {num_even}",
    ]

    if min_node is not None and max_node is not None:
        lines.append(f"- **Node value range:** {min_node} to {max_node}")

    # Trivial cycle information
    if num_cycles:
        lines.append(f"- **Cycles:** {num_cycles} (trivial cycle 1 → 2 → 4 → 1)")

    return "\n".join(lines)